How to work out oxidation numbers

Oxidation number is one of those SPM Chemistry skills that feels fiddly at first, then suddenly makes a whole chapter easier. Once you can assign it confidently you can name compounds with Roman numerals, spot which species is oxidised or reduced, and write half equations without guessing. This guide gives you the rules in the order you should apply them, then works through the examples that actually come up in redox equilibrium.

What an oxidation number really is

An oxidation number (or oxidation state) is a bookkeeping charge we assign to an atom, pretending every bond is fully ionic. It is written with the sign first, +2, −1, +7, which is the opposite order from an ionic charge like Fe²⁺. Keep that habit, because examiners notice.

The whole point is that when an atom’s oxidation number goes up, it has been oxidised; when it goes down, it has been reduced. That single idea sits underneath displacement, electrolysis and rusting.

The rules, in the order to use them

Apply these from the top. The first one that fixes an atom wins.

1. An uncombined element is 0. This covers Zn, Cu, O₂, Cl₂, S₈, any element on its own.
2. A monatomic ion equals its charge. Na⁺ is +1, Cl⁻ is −1, Al³⁺ is +3, S²⁻ is −2.
3. Group 1 metals are +1, Group 2 metals are +2, aluminium is +3 in their compounds.
4. Fluorine is always −1 in compounds.
5. Hydrogen is +1 in most compounds (but −1 in metal hydrides such as NaH).
6. Oxygen is −2 in most compounds (but −1 in peroxides such as H₂O₂).
7. The sum of all oxidation numbers in a neutral compound is 0. In a polyatomic ion, the sum equals the ion’s charge.

Rule 7 is the workhorse. You fix every atom you can with rules 1–6, then let rule 7 solve for the unknown.

Worked example 1: manganese in KMnO₄

Potassium permanganate is a classic exam species. Fix what you know:

• K is Group 1, so +1.
• Each O is −2, and there are four, giving 4 × (−2) = −8.
• The compound is neutral, so everything sums to 0.

So (+1) + Mn + (−8) = 0, which gives Mn = +7. That very high oxidation number is why KMnO₄ is such a strong oxidising agent.

Worked example 2: sulfur in H₂SO₄

Sulfuric acid, from the contact process:

• Two H at +1 each = +2.
• Four O at −2 each = −8.
• Neutral compound sums to 0.

So (+2) + S + (−8) = 0, giving S = +6.

Worked example 3: a polyatomic ion, Cr₂O₇²⁻

Here the sum is not 0 but the ion charge, −2:

• Seven O at −2 = −14.
• Let each Cr be x, and there are two of them: 2x.
• 2x + (−14) = −2, so 2x = +12 and Cr = +6.

Notice the oxidation number is +6 for each chromium, not +12, always divide back down to a single atom.

Worked example 4: nitrogen in NH₃ and NH₄⁺

In ammonia NH₃: three H at +1 = +3, compound neutral, so N = −3. In the ammonium ion NH₄⁺: four H at +1 = +4, and the ion is +1, so N + (+4) = +1, giving N = −3 again. Same nitrogen, same oxidation number.

Using oxidation numbers to name compounds

The Roman numeral in a name is the oxidation number of the metal. Iron(II) chloride is FeCl₂ (Fe is +2); iron(III) chloride is FeCl₃ (Fe is +3). Copper(II) oxide is CuO. When a metal has more than one common oxidation number, SPM expects the Roman numeral, so working it out is not optional.

Using oxidation numbers to spot redox

Take zinc displacing copper from copper(II) sulfate, a reaction you meet in displacement of metals:

Zn + Cu²⁺ → Zn²⁺ + Cu

• Zinc goes from 0 to +2, its oxidation number rose, so zinc is oxidised (it is the reducing agent).
• Copper goes from +2 to 0, its oxidation number fell, so copper(II) is reduced (it is the oxidising agent).

Because zinc sits above copper in the electrochemical series, it loses electrons more readily, so the direction is exactly what the series predicts. Tracking the numbers up and down is the fastest way to identify the oxidising and reducing agents in any equation.

Common mistakes to avoid

• Writing the sign last. Oxidation number is +2, not 2+. Get the order right every time.
• Forgetting to multiply by the number of atoms. Four oxygens is −8, not −2.
• Not dividing back to one atom. Cr₂O₇²⁻ gives 2x = +12, so each Cr is +6.
• Using −2 for oxygen in a peroxide. In H₂O₂ oxygen is −1.

Practise until the rules are automatic

The method never changes: fix every atom you can from the rules, then let the total do the rest. Drill it on nitrates, sulfates, permanganate and dichromate until you barely think about it, then use it to label redox reactions. If the sign convention or the harder ions keep tripping you up, that is a quick thing to fix with a teacher, our online one-to-one lessons run in English from RM50 an hour, with a paid one-hour trial, and we drill oxidation numbers against real Paper 2 questions. See how it works if that would help.